The inequality x ≤ -5 or x ≥ 3 in interval notations is (-∞, -5] ∪ [3, ∞)
Inequality is the relationship between two expressions or values that are not equal to each other
The inequality x ≤ -5 or x ≥ 3 represents the solution set of all real numbers less than or equal to -5 or greater than or equal to 3.
The interval notation of the given inequality is (-∞, -5] ∪ [3, ∞)
The closed brace means the number is included and open bracket doesnot includes a number
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Your income is R18 000 per month. How much can you pay on a house? (1)
The amount more in income tax that Cho pays than Helen each month would be £56.
Here, we have,
First, find Helen's yearly salary :
= 1, 720 x 12
= £ 20, 640
Both Cho's and Helen's annual salaries fall within the Basic rate tax bracket.
Cho 's monthly tax would be:
= (( 24, 000 - 12, 570 ) x 20 % ) / 12
= £ 190. 50
Helen's monthly tax :
= (( 20, 640 - 12, 570 ) x 20 % ) / 12
= £ 134.50
The difference is therefore :
= 190. 50 - 134.50
= £56
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complete question:
You can use these steps to work out the amount of income tax you pay each month.
Work out
monthly salary - 987.5
Work out
answer to Step 1 +5
Step 1
Step 2
Cho has a salary of £24 000 per year.
Helen has a salary of £1720 per month.
How much more income tax does Cho pay than Helen each month?
Maricopa's Success scholarship fund receives a gift of $ 195000. The money is invested in stocks, bonds, and CDs. Stocks pay 10.1 % interest, bonds pay 4.8 % interest, and CDs pay 4.75 % interest. Maricopa Success invests $ 35000 more in bonds than in CDs. If the annual income from the investments is $ 13580 , how much was invested in each account?
Maricopa Success invested $ in stocks.
Maricopa Success invested $ in bonds.
Maricopa Success invested $ in CDs.
Using a system of equations, the investments in each account are as follows:
Maricopa Success invested $80,000 in stocks.
Maricopa Success invested $75,000 in bonds.
Maricopa Success invested $40,000 in CDs.
What is a system of equations?A system of equations is two or more equations solved simultaneously, concurrently, or at the same time.
The total scholarship fund received = $195,000
The earnings from the investments:
Stocks = 10.1% = 0.101
Bonds = 4.8% = 0.048
CDs = 4.75% = 0.0475
Let the amount invested in CDs = x
Let the amount invested in Bonds = x + 35,000
Let the amount invested in stocks = y
The annual income from the investments = $13,580
Forming Equations:x + x + 35,000 + y = 195,000
2x + 35,000 + y = 195,000
2x + y = 160,000 ... Equation 1
0.101y + 0.048x + 1,680 + 0.0475x = 13,580
0.0955x + 0.101y = 11,900 ... Equation 2
Multiply Equation 1 by 0.101:
0.202x + 0.101y = 16,160 ... Equation 3
Subtract Equation 2 from Equation 3:
0.202x + 0.101y = 16,160
-
0.0955x + 0.101y = 11,900
0.1065x = 4,260
x = 40,000
Substitute x = 40,000 in Equation 1:
2x + y = 160,000
2(40,000) + y = 160,000
80,000 + y = 160,000
y = 80,000
Investment in CDs = $40,000
Investment in Bonds = $75,000 ($40,000 + $35,000)
Investment in Stocks = $80,000
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$150 reduced by 33 1/3%
Hello,
150 - 1/3% of 150
= 150 - 33,33% x 150
= 150 - 50
= 100
approximately 100
Example: 33 1/3% = 1/3. 1/3 of $150.00 = $50.00, so discounted price is: $150.00 - $50.00 = $100.00
x is an acute angle. Find the value of x in degrees. sin(x)=0.1 Write your answer as an integer or as a decimal rounded to the nearest hundredth. x=
X is an acute angle x = 5.74 degrees (rounded to the nearest hundredth) would be the appropriate answer for an acute angle satisfying sin(x) = 0.1.
To find the value of x in degrees when sin(x) = 0.1, we can use inverse trigonometric functions. Specifically, we can use the arcsin function to determine the angle whose sine is 0.1.
Using a scientific calculator or a trigonometric table, we can find the arcsin of 0.1. This gives us approximately 5.739 degrees.
However, since x is an acute angle, it means that x is between 0 and 90 degrees. The value 5.739 degrees falls within this range.
Therefore, the value of x in degrees, when sin(x) = 0.1 and x is an acute angle, is approximately 5.739 degrees.
Rounded to the nearest hundredth, the value of x would be 5.74 degrees.
It's important to note that the arcsin function has a range from -90 degrees to 90 degrees. In this case, since we are looking for an acute angle, we consider only the positive solution.
So, x = 5.74 degrees (rounded to the nearest hundredth) would be the appropriate answer for an acute angle satisfying sin(x) = 0.1.
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El costo de un terreno es IP al cuadrado de la distancia que lo separa de Lima y DP a su área. Un terreno cuesta 540 mil y otro de doble área que está situado a una distancia 3 veces mayor que la distancia anterior, ¿qué precio tendrá?
Answer:60,000
Step-by-step explanation:
El costo de un terreno es IP al cuadrado de la distancia que lo separa de Lima y DP a su área. Esto se puede expresar como:
Costo = IP^2 * DP / Distancia^2
Sabemos que el costo de un terreno es de 540 mil, por lo que podemos escribir:
540,000 = IP^2 * DP / Distancia^2
Ahora consideremos el segundo terreno, que tiene el doble de área y está a una distancia 3 veces mayor que la del primer terreno. Si llamamos "Distancia anterior" a la distancia del primer terreno, entonces la distancia del segundo terreno es 3 veces la distancia anterior, es decir:
Distancia = 3 * Distancia anterior
Además, sabemos que el segundo terreno tiene el doble de área que el primero, por lo que podemos escribir:
Área = 2 * Área anterior
Reemplazando estas expresiones en la ecuación anterior, obtenemos:
Costo = IP^2 * DP / (3 * Distancia anterior)^2
Simplificando:
Costo = IP^2 * DP / 9 * Distancia anterior^2
Pero sabemos que el costo del segundo terreno es lo que estamos buscando. Llamemos "Precio del segundo terreno" a este valor. Entonces:
Precio del segundo terreno = IP^2 * DP / 9 * Distancia anterior^2
Como el costo del primer terreno es 540 mil, podemos reemplazar los valores conocidos:
540,000 = IP^2 * DP / Distancia anterior^2
Despejando IP^2, tenemos:
IP^2 = 540,000 * Distancia anterior^2 / DP
Reemplazando esta expresión en la ecuación anterior, obtenemos:
Precio del segundo terreno = (540,000 * Distancia anterior^2 / DP) * DP / 9 * Distancia anterior^2
Simplificando:
Precio del segundo terreno = 60,000 / DP * 2
Por lo tanto, el precio del segundo terreno es de 60,000 dividido por dos veces el valor de DP.
What’s the answer to v/7=-19/7
Answer: v=-19
Step-by-step explanation:
We can multiply by 7 on both sides which cancels out 7 on both sides. He new equation would be v=-19 which is our answer.
the number line represents values for X which inequality Best describes the included values
picture also includes the answers
The inequality that best describes the included values of x is x < 8
Stating the inequality that best describes the included values of xFrom the question, we have the following parameters that can be used in our computation:
The number line
On the number line, we have the following
Open circle on 8Arrow points to the left of 8The above means that we make use of the less than symbol
This is because the open circle uses < or > while arrows pointing left means <
So, we have
x < 8
Hence, the inequality that best describes the included values of x is x < 8
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Compare the functions shown below: f(x) = (x + 3)2 − 2 g(x) linear graph with y intercept of negative 3 over 2 and x intercept of 3 h(x) x y −3 2 −2 7 −1 14 0 23 1 34 2 47 3 62 What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = −1 to x = 3? Group of answer choices f(x), g(x), h(x) g(x), f(x), h(x) h(x), g(x), f(x) g(x), h(x), f(x)
The correct order of the functions from least to greatest is g(x), f(x) and h(x).
The given function is f(x)=(x+3)²-2.
g(x) linear graph with y-intercept = c = -3/2 and x-intercept = 3
f (x) = (x + 3)² - 2
For x = -1
f (-1) = (-1 + 3)² - 2
f (-1) = (2)² - 2
f (-1) = 4 - 2
f (-1) = 2
For x = 3
f(3) = (3 + 3)² - 2
f(3) = (6)² - 2
f(3) = 36 - 2
f(3) = 34
AVR = ((34) - (2))/((3) - (- 1))
AVR = 8
For g(x):
linear graph with and intercept of negative 3 over 2 and x intercept of 3
y = mx + b
b = -3/2
For me we have:
0 = m (3) - 3/2
3m = 3/2
m = 1/2
The function g(x) is:
g (x) = (1/2) x - 3/2
For x = -1
g (-1) = (1/2) (- 1) - 3/2
g (-1) = -1/2 - 3/2
g (-1) = -4/2
g (-1) = -2
For x = 3
g (3) = (1/2) (3) - 3/2
g (3) = 3/2 - 3/2
g (3) = 0
AVR = ((0) - (- 2)) / ((3) - (- 1))
AVR = 1/2
For h(x):
Using the table we have:
AVR = ((62) - (14)) / ((3) - (- 1))
AVR = 12
From least to greatest g(x), f(x), h(x)
Therefore, the correct order of the functions from least to greatest is g(x), f(x) and h(x).
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An isotope of cobalt-60, is used in medical therapy. When the radioisotope activity has decreased to 45% of its initial level, the exposure times required are too long and the hospital needs to replace the cobalt. How often does the cobalt need to be replaced if the half-life of cobalt-60 is 5.24 years? Round your answer to the nearest whole number
The hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.
The half-life of cobalt-60 is 5.24 years, which means that after 5.24 years, the radioisotope activity will have decreased to 50% of its initial level. Since the hospital needs to replace the cobalt when the radioisotope activity has decreased to 45% of its initial level, this means that the cobalt needs to be replaced after slightly less than one half-life has passed.
To find out how long this is, we can use the formula:
t = (ln(0.45) / ln(0.5)) x 5.24
where t is the time in years since the cobalt was first used.
Using a calculator, we find that:
t ≈ 2.16 years
Therefore, the hospital needs to replace the cobalt approximately every 2.16 years. Rounded to the nearest whole number, this is 2 years.
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Please help and explain, I'm not getting this at all
The quotient function for this problem is given as follows:
(f/g)(x) = (x + 2)/(2x² + 4x - 5)
How to obtain the quotient function?The functions f(x) and g(x) have the definitions presented as follows:
f(x) = x + 2.g(x) = 2x² + 4x - 5.To obtain the quotient of the two functions, we simply divided the definition of the function f(x) by the definition of the function g(x).
Both functions are defined on the bullet point, hence the quotient function for this problem is given as follows:
(f/g)(x) = (x + 2)/(2x² + 4x - 5)
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Helppp pleasseeee guys
When we apply Gauss- Jordon elimination method to solve the system of equation, it becomes;
[tex]\left[\begin{array}{cccc}1&0&0&6\\0&1&0&2\\0&0&1&-6\end{array}\right][/tex]
How do we solve the linear equation is Gauss- Jordon elimination method?To solve the augment matrix that represents a system of linear equation using Gauss- Jordon elimination method, we reduce every value to 0's and 1's to get the values in the fourth column.
-5 -3 -4 -12
0 -2 -7 38
0 1 4 -22
R₁ ÷ -5 R₂ ÷ -2
1 3/5 4/5 12/15 1 3/5 4/5 12/15
0 -2 -7 38 0 1 7/2 -19
0 1 4 -22 0 1 4 -22
R₁ - 3/5R₂ 2R₃
1 0 -13/10 69/5 1 0 -13/10 69/5
0 1 7/2 -19 0 1 7/2 -19
0 0 1/2 -3 0 0 1 -6
R₂ + 13/10R₃ R₂ - 7/2R₃
1 0 0 6 1 0 0 6
0 1 7/2 -19 0 1 0 2
0 0 1 -6 0 0 1 -6
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Find lower and upper bounds for the area between the z-axis and the graph of f(x) = √x+3
over the interval [-1, 1] by calculating left-endpoint and right-endpoint Riemann sums with 4
subintervals. The graphs of L4 and R4 are given below.
Answer:
L4 = 3.299R4 = 3.592Step-by-step explanation:
You want the left sum and the right sum of the four subinterval areas under the curve f(x) = √(x+3) on the interval [-1, 1].
Riemann sumThe Riemann sum is the sum of the subinterval areas. The area of each subinterval is the height of the rectangular area, multiplied by its width. Here, the interval width is (1 -(-1))/4 = 0.5.
The heights of the intervals of interest will be the function values f(-1 +0.5n) for f(x) = √(x+3) and n = 0 .. 3 for the left sum and 1 .. 4 for the right sum.
ValuesThe attached calculator display shows the function values for n=0 .. 4. The expression Total(Most( )) adds the first four function values; while the expression Total(Rest( )) adds the last four function values of these five. Multiplying by the interval width (1/2) gives the left- and right-Riemann sums, respectively.
Lower Bound (L4) = 3.299Upper Bound (R4) = 3.592__
Additional comment
The actual integral value is about 3.44772.
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Just need help on these two questions please
Determine the value of f (3) for the function. Please help, answer is not 0
The value of f(3) in the function is undefined
The given function are f(x)= x³+18x²+104x+192 for x≤-3
f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3
f(x)= 3x-9/x³-2x²-5x+6 for -3< x≤3
f(x)=√x²-9
We have to find the value of f(3)
The 3 lies in the interval -3< x≤3
So we use function f(x)= 3x-9/x³-2x²-5x+6 to find f(3)
f(x)= 3(3)-9/(3)³-2(3)²-5(3)+6
=0/27-18-15+6
=undefined
Hence, the value of f(3) in the function is undefined
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Help for my math homework
Answer:
82 in^2
Step-by-step explanation:
Total Surface Area (TSA) = 2 × Base Area + Base Perimeter × Height
TSA = 2× (7×2) + (7+7+2+2) ×3
= 2 × 14 + 18 × 3
= 82 in^2
Imymaths Kinematics formulae, need help desperately
1. The final velocity is 8.3 m/s and the distance covered is 16.8 m.
2. The acceleration is 34.7 and it would travel 58.9 m.
What is the acceleration?Acceleration is a physical quantity that describes the rate of change of an object's velocity over time. In other words, it is the rate at which the speed or direction of motion of an object changes.
Using;
v = u + at
v = ?
u = 2.9 m/s
a = 1.8 m/s2
t = 3 s
Then;
v = 2.9 + (1.8 * 3)
v = 8.3 m/s
Also;
[tex]v^2 = u^2 + 2as\\s = v^2 - u^2/2a\\s = (8.3)^2 - (2.9)^2/2 * 1.8[/tex]
s = 68.89 - 8.41/3.6
= 16.8 m
2)
[tex]v^2 = u^2 + 2as\\a = v^2 - u^2/2s\\a = (27)^2 - 0^2/2 * 10.5[/tex]
a = 34.7[tex]m/s^2[/tex]
Using;
[tex]s = ut + 1/2at^2\\ut = 0\\s = 1/2at^2\\s = 0.5 * 34.7 * (2)^2\\s = 69.4 m[/tex]
It would travel; 69.4 - 10.5 = 58.9 m
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Evaluate the integral
heeeeelp
The value of the indefinite integral in the context of this problem is given as follows:
B. [tex]\cosh{(e^x + 5)} + C[/tex]
How to solve the indefinite integral?The indefinite integral in the context of this problem is defined as follows:
[tex]\int e^x \sinh{(e^x + 5)} dx[/tex]
We can use substitution to solve the integral, hence:
[tex]u = e^x + 5[/tex]
[tex]du = e^x dx[/tex]
[tex]dx = \frac{du}{e^x}[/tex]
Hence the integral as a function of u is given as follows:
[tex]\int \sinh{u} du[/tex]
The result of the integral is of:
cosh(u) + C.
In which C is the constant of integration.
As a function of x, the integral is given as follows:
[tex]\cosh{(e^x + 5)} + C[/tex]
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find the coordinates
Answer:
2?
Step-by-step explanation:
Whats the answer to x^7 divide x^2
The simplification of the given expression above would be = x⁵
What are exponential laws in mathematics?The exponential laws in mathematics states that to multiply two exponential functions with the same base, we simply add the exponents.
The second law states that to divide two exponential functions with the same base, we subtract the exponents.
From the expression given above;
x⁷/x² = X(7-2) = x⁵
Therefore, in conclusion, the simplification of the given expression above while following the guide of the exponential laws would be = x⁵
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In the football game, a penalty of -15 yards was applied to a gain of 43 yards. What was the net gain?
A = 58 yards
B = 32 yards
C = 28 yards
D = 18 yards
A prospector graphed the locations of a gold vein and all of the gold dust strikes in the vicinity. He positioned the gold vein at (-2,7) and the farthest gold dust strike at (74,7). If each unit on the graph
represents 1 mile, then how far away from the gold vein is the farthest gold dust strike?
miles
The farthest gold dust strike is 76 miles away from the gold vein.
The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by:
d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ²
As per the question, we have to find the distance between the gold vein at (-2, 7) and the farthest gold dust strike at (74, 7).
Substituting the values into the distance formula, we have:
d = √((74 - (-2))² + (7 - 7)²)
d = √(76²)
d = 76
Therefore, the farthest gold dust strike is 76 miles away from the gold vein.
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ind the areas of the sectors formed by \angle ACB .
A circle is shown. The measure of central angle A C B is 131 degrees. The radius is 3 centimeters. Point D is on the circle but not on arc A B.
Give the exact answers in terms of \pi . Do not approximate the answers.
Area of small sector =
cm2
Area of large sector =
cm2
solve |x-3| if x>5 HELP ME!!!!!!!!!!
Answer:
Step-by-step explanation:
chill
If x > 5, then x - 3 > 0 since x is greater than 3. Therefore, |x - 3| = x - 3.
will mark brainliest
when the function f(x) = 2x^n + ax² - 6 is divided by (x+3), the remainder is 129.
calculate the value of "a" and "n" and hence write the complete polynomial function.
The complete polynomial is f(x) = 2x³ + 15x² - 6 if n = 3 and a = 15
Given is polynomial f(x) = 2xⁿ + ax² - 6, when divided by (x+3), the remainder is 129,
Calculating the values of a and n :-
From the question, we have the following parameters that can be used in our computation:
f(x) = 2xⁿ + ax² - 6 is divided by (x+3), the remainder is 129
This means that,
f(-3) = 129
So, we have
f(-3) = 2(-3)ⁿ + a(-3)² - 6
f(-3) = 2(-3)ⁿ + 9a - 6
2(-3)ⁿ + 9a - 6 = 129
2(-3)ⁿ + 9a = 135
Assume n = 3
So, we have
2(-3)³ + 9a = 135
2/27 + 9a = 135
9a = 135 - 2/27
9a = 3643/27
a = 3643/243
a = 15
Therefore,
n = 3 and a = 15
So, the complete polynomial is f(x) = 2x³ + 15x² - 6
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Find f(-3) for the piecewise function:
We need to use the first part of the function, we can see that:
f(-3) = 0
The correct option is the third one.
How to find the value of f(-3)?Here we have a piecewise function. It means that the function behaves differently on different parts of its domain.
Here we want to evalaute the function in x = -3, so we need to find which of the parts of the function we need to use.
We can see that:
f(x) =x + 3 if x ≤ 0
and -3 is smaller than zer, so we need to use this one.
Then:
f(-3) = -3 + 3 = 0
The correct option is the third one.
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Let Π be the plane containing the linex= 1 + 2t, y=−1 + 3t, z= 4 +t and parallel to the vector〈0,2,1〉.
(1) Find the equation of the plane Π.
(2) Find the equation of the plane Π1 that is parallel to Π and passes through (2,2,2).
(3) Find the distance between Π and Π1.
a) The equation of the plane is 2y + z - 2 = 0.
b) The equation of the plane Π1 that is parallel to Π and passes through (2,2,2) is 2y + z - 6 = 0.
c) The distance between the planes Π and Π1 is 4 / √6.
Given data ,
The given line has the parametric equations:
x = 1 + 2t
y = -1 + 3t
z = 4 + t
By comparing the coefficients of t, we can identify a point on the line, which is (1, -1, 4) when t = 0.
To find the normal vector to the plane Π, we use the fact that it is parallel to the vector ⟨0, 2, 1⟩. Since the normal vector is perpendicular to the plane, any vector parallel to the plane can serve as the normal vector. Therefore, we can take the vector ⟨0, 2, 1⟩ as the normal vector.
Now we have a point (1, -1, 4) on the plane Π and a normal vector ⟨0, 2, 1⟩.
The equation of the plane Π can be written as:
0(x - 1) + 2(y + 1) + 1(z - 4) = 0
Simplifying the equation gives:
2y + z - 2 = 0
So, the equation of the plane Π is 2y + z - 2 = 0.
(2)
To find the equation of the plane Π1 that is parallel to Π and passes through (2, 2, 2), we can use the same normal vector ⟨0, 2, 1⟩.
The equation of the plane Π1 can be written as:
0(x - 2) + 2(y - 2) + 1(z - 2) = 0
Simplifying the equation gives:
2y + z - 6 = 0
So, the equation of the plane Π1 is 2y + z - 6 = 0.
(3)
We can take the point (1, -1, 4) on the plane Π and find the perpendicular distance from this point to the plane Π1 using the equation of Π1.
The distance between the two planes is given by the formula:
Distance = |Ax₀ + By₀ + Cz₀ + D| / √(A² + B² + C²)
Using the point (1, -1, 4) and the equation of Π1: 2y + z - 6 = 0, we can substitute the values into the formula:
Distance = |(2)(-1) + (1)(4) - 6| / √(2² + 1² + 1²)
= |(-2) + 4 - 6| / √(4 + 1 + 1)
= |-4| / √6
= 4 / √6
Hence , the distance between the planes Π and Π1 is 4 / √6.
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A student is creating a graph to represent the equation y=2/3x-5. Which point is not on the line represented by the students graph? A. (9,1) B. (12,7) C. (15,5) D. (21,9)
Answer: B. (12, 7)
Step-by-step explanation: If we substitute the x values in the equation the answer has to equal the y value of the coordinate. If we substitute 12 for the x we get y = 3. So answer B is the coordinate not represented by the student's graph.
Darlene places $500 in a savings account that pays 4% interest. The amount, t years after 2005, can be modeled by the following equation. Elisa places $600 in a savings account that pays 5% interest. The amount, t years after 2005, can be modeled by the following table. t 0 5 10 15 20 f(t) $600 $766 $977 $1,247 $1,592 Based on these values, which account has the greater average rate of change between 2005 and 2015?
Elisa's savings account has the greater average rate of change between 2005 and 2015.
How to explain the rateFor Darlene's savings account, the initial amount in 2005 is $500. To calculate the value of the account in 2015, we need to know how many years have passed. Since 2015 is 10 years after 2005, we can substitute t = 10 into the equation given:
f(t) = 500(1 + 0.04t)
f(10) = 500(1 + 0.04(10))
f(10) = 500(1.4)
f(10) = 700
Therefore, the amount in Darlene's savings account in 2015 is $700. The average rate of change between 2005 and 2015 is the slope of the line connecting the points (0, 500) and (10, 700):
slope = (700 - 500) / (10 - 0) = 20
For Elisa's savings account, we are given the values of the function at several points, but we need to determine the slope of the line connecting the points (0, 600) and (10, 977), since this represents the change between 2005 and 2015. The slope is:
slope = (977 - 600) / (10 - 0) = 37.7
Therefore, Elisa's savings account has the greater average rate of change between 2005 and 2015.
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On a test, the highest grade was 40.5 points higher then the lowest grade. The sum of the two grades was 138. Find the lowest grade.
Answer:
48.75
Step-by-step explanation:
call highest H and lowest L
H = L + 40.5
sum of them = 138
H + L = 138
(L + 40.5) + L = 138
2L + 40.5 = 138
2L = 138 - 40.5 = 97.5
L = 48.75
I need to know surface area
Answer: 165 ft squared
Step-by-step explanation:
1. First find the area of the bottom face (you don’t need to divide by two because the other triangle makes the one on the bottom a full rectangle.)
10x4.5=45
2. Find area of face facing you. (The lateral one, rectangle face)
10x5=50
3. Find area of left and right lateral faces (its at the back)
6x5=30
8x5=40
4. Add all answers to get total surface area
40+30+50+45=165
5.Add unit and then celebrate because you did it!
165 ft squared
Hope this helps!
